Influences of Poroelasticity on Wave Propagation: A Time Stepping Boundary Element Formulation: Fid-Bau Portal

Influences of Poroelasticity on Wave Propagation: A Time Stepping Boundary Element Formulation

Pryl, Dobromil

Wave propagation phenomena in poroelastic continua are modeled with a Boundary Element (BE) formulation based on Biots theory. The Convolution Quadrature Method (CQM) makes it possible to use the available Laplace domain fundamental solutions in a time domain BE formulation. Support for 2-d problems has been added to the existing 3-d implementation. Further, a formulation for incompressible constituents and mixed elements have been implemented and tested. In a two-phase material not only each constituent, the solid and the fluid, may be compressible on the microscopic level but also the skeleton itself possesses a structural compressibility. If the compression modulus of a constituent is much larger than the compression modulus of the bulk material, this constituent is assumed to be materially incompressible. The fundamental solutions for incompressible poroelasticity in both 2-d and 3-d are derived using the method of Hörmander. Numerical experiments show that there are no noticeable differences for some materials (e.g., soil), and then the incompressible model can be recommended to obtain a speedup of about 20 percent. In the conventional BEM implementation, the same shape functions are applied to all state variables. Motivated by the improvements due to mixed elements in FEM, i.e. the shape function for the pressure is chosen one degree lower than for the displacement, such elements have been added to the BEM implementation. A study about the influence of the mixed shape functions to the quality of numerical results and the stability of the time-stepping scheme shows that the mixed elements can only be recommended in special cases in BEM. The proposed formulation is validated by comparison to a 1-d analytical solution. A poroelastic halfspace is modeled in both 2-d and 3-d numerical experiments to study wave propagation with emphasis on surface waves. The influence of material incompressibility on various wave types is also examined.